American Journal of Computational and Applied Mathematics

American Journal of Computational and Applied Mathematics is a peer-reviewed international journal. This journal publishes significant research papers from all branches of applied mathematical and computational sciences. It publishes original papers of high scientific value in all areas of computational and applied mathematics.

Hemant Kumar Pathak

Editorial Board Member of American Journal of Computational and Applied Mathematics

Professor, Pt. Ravishankar Shukla University, India

Research Areas

Nonlinear Analysis, Approximation Theory, Operator Theory, Number Theory, Cryptography, Integration Theory, Summability Theory, Control Theory, Fuzzy Set Theory

Education

1988Ph.DMathematics from Pt. Ravishankar Shukla University, Raipur
1977M.ScMathematics from Pt. Ravishankar Shukla University, Raipur
1975B.ScPt. Ravishankar Shukla University, Raipur
1971HSSCHSSC from M.P.Board of Secondary Education, Bhopal (M.P.)

Experience

2005-presentProfessor, Pt. Ravishankar Shukla University, Raipur (C.G.)
1991-2005Assist.Professor (Selection Grade), Kalyan Mahavidyalaya, Bhilai Nagar (C.G.)
1986-1991Assist. Professor (Senior Grade), Kalyan Mahavidyalaya, Bhilai Nagar (C.G.)
1978-1986Lecturer/Assist. Professor(1982 onward), Kalyan Mahavidyalaya, Bhilai Nagar (C.G.)
1978Ad-hoc Lecturer, Govt. Post-Graduate College, Dhamtari

Membership

American Mathematical Society (USA)-Member (1991-1995)
International Federation of Nonlinear Analysts (USA)-Member (1996-2008)
Indian Sciences Congress Association-(1985-86)
Allahabad Mathematics Society-Life Member
Bharat Ganit Parishad-Life Member
The Vijnana Parisad of Indian-Life Member
Calcutta Mathematical Society-Life Member
National Academy of Mathematics-Life Member

Publications: Journals

[1]  MR2677333 Pathak, H. K.; Tiwari, Satyaj Common fixed point and best simultaneous approximations for Ciric type (f, g)-weak contraction and weak asymptotic contraction. Int. J. Pure Appl. Math. 62 (2010), no. 3, 291–304, 54H25 (Bulgaria)
[2]  MR2656374 Pathak, H. K.; Tiwari, Satyaj Best simultaneous approximation via KKM-mapping method for multivalued mappings. Int. J. Pure Appl. Math. 59 (2010), no. 2, 181–190, 46B99 (41A65 47H04) (Bulgaria)
[3]  MR2609270 Suzuki, Tomonari; Pathak, Hemant Kumar Almost biased mappings and almost compatible mappings are equivalent under some condition. J. Math. Anal. Appl. 368 (2010), no. 1, 211–217. (Reviewer: Helga Fetter), 47H10 (Elsevier)
[4]  MR2583316 Pathak, H. K.; Tiwari, Satyaj On best simultaneous approximation in semi metric spaces. J. Concr. Appl. Math. 8 (2010), no. 4, 623–630, 41A65 (54E35) (USA)
[5]  MR2672032 Pathak, H. K. Integral Φ-type contractions and existence of continuous solutions for nonlinear integral inclusions. Nonlinear Anal. 71 (2009), no. 12, e2577–e2591, 45P05 (47H10 47N20) (Elsevier)
[6]  MR2647787 Pathak, H. K.; Singh, Prachi Generalization of a fixed point theorem for weakly compatible mapping. Math. Sci. Res. J. 13 (2009), no. 12, 286–291, 54H25 (54A40) (USA)
[7]  MR2604360 Pathak, H. K.; Verma, R. K. Common fixed point theorems for weakly compatible mappings on Menger space and application. Int. J. Math. Anal. (Ruse) 3 (2009), no. 21-24, 1199–1206, 54H25 (47H09 47H10 54E70) (Bulgaria)
[8]  MR2604359 Pathak, H. K.; Verma, R. K. An integral type implicit relation for converse commuting mappings. Int. J. Math. Anal. (Ruse) 3 (2009), no. 21-24, 1191–1198, 54H25 (47H09 47H10) (Bulgaria)
[9]  MR2604358 Pathak, H. K.; Verma, R. K. Integral type contractive condition for converse commuting mappings. Int. J. Math. Anal. (Ruse) 3 (2009), no. 21-24, 1183–1190, 54H25 (47H09 47H10) (Bulgaria)
[10]  MR2566510 (2010k:54060) Pathak, H. K.; Shahzad, N. Fixed point results for generalized quasicontraction mappings in abstract metric spaces. Nonlinear Anal. 71 (2009), no. 12, 6068–6076, 54H25 (47H10) (Elsevier)
[11]  MR2571447 Jha, K.; Pant, R. P.; Pathak, H. K. A common fixed point theorem for generalized contractive type mappings. Uzbek. Mat. Zh. 2009, no. 2, 85–91, 47H10 (47H09) (Uzbekistan)
[12]  MR2555454 Pathak, H. K.; Rodriguez-López, Rosana; Singh, Prachi A common fixed point theorem for weakly compatible mappings and its application. J. Fuzzy Math. 17 (2009), no. 3, 699–710, 54A40 (54H25) (USA)
[13]  MR2540691 Fisher, B.; Pathak, H. K.; Tiwari, R. Common fixed point theorems. Thai J. Math. 7 (2009), no. 1, 137–150, 54H25 (47H10) (Thailand)
[14]  MR2540689 (2010i:54052) Pathak, H. K.; Verma, R. K.; Fisher, B. Fixed point and coincidence point theorems on Banach spaces over topological semifields and their applications. Thai J. Math. 7 (2009), no. 1, 115–127, 54H25 (47H10) (Thailand)
[15]  MR2534195 (2010h:41047) Pathak, H. K.; Khan, M. S. Common fixed point results and its applications to best approximation in ordered semi-convex structure. Bull. Math. Anal. Appl. 1 (2009), no. 1, 30–48. (Reviewer: Duran Turkoglu), 41A65 (41A50 47H10 54H25) (Crotia)
[16]  MR2541041 (2010i:54051) Pathak, Hemant Kumar; Shahzad, Naseer Gregus type fixed point results for tangential mappings satisfying contractive conditions of integral type. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 2, 277–288. (Reviewer: Louis A. Talman), 54H25 (47H10) (Belgium)
[17]  MR2499805 Pathak, H. K.; Khan, M. S. On best simultaneous approximation in ε-chainable metric spaces. J. Concr. Appl. Math. 7 (2009), no. 3, 276–280, 41A50 (41A28 41A65 47H10) (USA)
[18]  MR2499730 (2010d:54060) Pathak, H. K.; Shahzad, N. Fixed point results for set-valued contractions by altering distances in complete metric spaces. Nonlinear Anal. 70 (2009), no. 7, 2634–2641. (Reviewer: S. L. Singh), 54H25 (47H10) (Elsevier)
[19]  MR2499055 Pathak, H. K.; Rodríguez-López, Rosana Some results on common fixed points for weakly compatible mappings satisfying Altman integral type contraction. Demonstratio Math. 42 (2009), no. 1, 143–162, 54H25 (47H10) (Poland)
[20]  MR2492131 (2010c:47171) Pathak, H. K.; Cho, Y. J.; Kang, S. M. Strong and weak convergence theorems for nonself-asymptotically perturbed nonexpansive mappings. Nonlinear Anal. 70 (2009), no. 5, 1929–1938, 47H10 (47H09 47J25) (Elsevier)
[21]  MR2488410 (2009k:54075) George, Reny; Khan, M. S.; Pathak, H. K. On commutativity and its generalizations in hybrid fixed point theory. Nonlinear Funct. Anal. Appl. 13 (2008), no. 1, 29–41, 54H25 (47H10 54C60) (S.Korea)
[22]  MR2482648 (2009m:54064) Pathak, H. K.; Verma, R. K. Weakly compatible mappings and Altman type contraction. Filomat 22 (2008), no. 1, 33–46. (Reviewer: Ion Marian Olaru), 54H25 (47H10) (Serbia)
[23]  MR2452090 (2009j:47123) Pathak, H. K.; Hussain, N. Common fixed points for Banach operator pairs with applications. Nonlinear Anal. 69 (2008), no. 9, 2788–2802. (Reviewer: Chika Moore), 47H10 (47J20 47N10 54H25) (Elsevier)
[24]  MR2447641 Pathak, H. K.; Verma, R. K. Coincidence and common fixed points in symmetric spaces under implicit relation and application. Int. Math. Forum 3 (2008), no. 29-32, 1489–1499, 54H25 (47H10)
[25]  MR2418584 Pathak, H. K.; Singh, Prachi Common fixed point theorems for fuzzy mappings in quasi-pseudo-metric space. Int. J. Math. Anal. (Ruse) 2 (2008), no. 1-4, 159–168, 54H25 (54A40)
[26]  MR2398641 (2009b:54048) Pathak, Hemant Kumar; Shahzad, Naseer Fixed points for generalized contractions and applications to control theory. Nonlinear Anal. 68 (2008), no. 8, 2181–2193, 54H25 (47H10 47N10 49L20) (Elsevier)
[27]  MR2378716 Pathak, H. K. Some problems and conjectures in number theory. Internat. J. Math. Ed. Sci. Tech. 39 (2008), no. 1, 77–82, 11A41 (UK)
[28]  MR2475390 Pathak, H. K.; Tiwari, Satyaj On best simultaneous approximation in metric spaces. J. Nonlinear Funct. Anal. Differ. Equ. 1 (2007), no. 2, 223–227, 41A28 (54H25) (India)
[29]  MR2391974 (2009f:54056) Pathak, H. K.; Khan, M. S. The homotopic invariance for fixed points of multivalued generalized φ-contractive maps. Nonlinear Funct. Anal. Appl. 12 (2007), no. 4, 531–562. (Reviewer: Wojciech Kryszewski), 54H25 (47H04 47H10 54C60) (S.Korea)
[30]  MR2380147 Pathak, H. K.; Singh, Prachi Common fixed point theorem for weakly compatible mapping. Int. Math. Forum 2 (2007), no. 57-60, 2831–2839, 54H25 (Bulgaria)
[31]  MR2358994 (2008g:47113) Pathak, H. K.; Rhoades, B. E.; Khan, M. S. Common fixed point theorems for asymptotically I-contractive mappings without convexity. Fixed Point Theory 8 (2007), no. 2, 285–296, 47H10 (54H25) (Romania)
[32]  MR2360891 Pathak, H. K.; Rodríguez-López, Rosana; Verma, R. K. A common fixed point theorem using implicit relation and property (E.A) in metric spaces. Filomat 21 (2007), no. 2, 211–234, 54H25 (47H10)
[33]  MR2346046 (2008f:47096) Pathak, Hemant Kumar; Tiwari, Rakesh; Khan, Mohammad Saeed A common fixed point theorem satisfying integral type implicit relations. Appl. Math. E-Notes 7 (2007), 222–228 (electronic). (Reviewer: Ljubomir B. Ćirić), 47H10 (54H25) (Taiwan China)
[34]  MR2333339 (2008f:45012) Pathak, H. K.; Khan, M. S.; Tiwari, Rakesh A common fixed point theorem and its application to nonlinear integral equations. Comput. Math. Appl. 53 (2007), no. 6, 961–971. (Reviewer: Wei-Zhong Zhao), 45G05 (47H10 47N20) (Elsevier)
[35]  MR2297802 Khan, M. S.; Pathak, H. K.; George, Reny Compatible mappings of type (A-1) and type (A-2) and common fixed points in fuzzy metric spaces. Int. Math. Forum 2 (2007), no. 9-12, 515–524, 54A40 (54H25)
[36]  MR2296348 (2008f:47095) Pathak, Hemant Kumar; Ume, Jeong Sheok Weakly compatible mappings and common fixed point theorems with applications to variational inequalities. Adv. Nonlinear Var. Inequal. 10 (2007), no. 1, 55–68. (Reviewer: Jen-Chih Yao), 47H10 (47J20 54H25) (USA)
[37]  MR2311572 Pathak, H. K.; Tiwari, Rakesh Fixed point theorems for expansion mappings satisfying implicit relations. Filomat No. 20, part 1 (2006), 43–57, 54H25 (Serbia)
[38]  MR2207685 (2006i:54054) Pathak, H. K.; Verma, R. K.; Kang, S. M.; Khan, M. S. Fixed points for weak compatible type and parametrically φ(ε, δ;a)-contraction mappings. Int. J. Pure Appl. Math. 26 (2006), no. 2, 247–263, 54H25 (47H09 47H10) (USA)
[39]  MR2196714 (2006h:54037) Kalinde, A. K.; Mishra, S. N.; Pathak, H. K. Some results on common fixed points with applications. Fixed Point Theory 6 (2005), no. 2, 285–301. (Reviewer: S. Swaminathan), 54H25 (47H10) (Romania)
[40]  MR2167112 Pathak, H. K.; Khan, M. S.; George, Reny Coincidence and common fixed points of non-self hybrid mappings in metrically convex spaces. Nonlinear Funct. Anal. Appl. 10 (2005), no. 2, 257–272, 54H25 (47H10 54C60) (S.Korea)
[41]  H.K.Pathak, R. Tiwari, A Gregus type common fixed point theorem in normed spaces with application, Banach J. Math. Anal. 5 (2011), n0. 1, 136-147. (Iran)
[42]  H.K.Pathak, N, Hussain, Common fixed points for P-operator pair with applications, Applied mathematics and Computation 217 (2010) 3137-3143. (Elsevier)
[43]  S.L.Singh, H.K.Pathak, S.N.Mishra, On a Suzuki type general fixed point theorem with applications, Fixed Point Theory and Applications, Volume 2010, Article ID 234717, 15 pages, doi:10.1155/2010/234717.(USA)
[44]  H.K.pathak, M.S.Khan, Jong Kyu Kim, Coincidence point and homotopy results for f-hybrid compatible maps, Nonlinear Functional Analysis and Applications, Vol. 15, No. 1(2010), pp. 87-162.(S. KOREA)
[45]  H.K.Pathak, M.Shanghi, Key exchange scheme with higher security and its analysis, African Journal of Mathematics and Computer Science Research Vol. 3(12), pp. 290-296, December 2010. (China)
[46]  H.K.Pathak, M.Shanghi, Speeding up computation of scalar multiplication in elliptic curve cryptosystem, International Journal on Computer Science and Engineering Vol. 02, No. 4, 2010, 1024-1028. (India)
[47]  H.K.Pathak, M.Shanghi, Public key cryptosysytem and a key exchange protocol using tools of non-abelian group, International Journal on Computer Science and Engineering Vol. 02, No. 4, 2010, 1029-1033. (India)
[48]  H.K.Pathak, A Note on Convergence of a Sequence and its Applications to Geometry of Banach Spaces, Advances in Pure Mathematics , Vol. 1 , No. 3 (2011), to appear.(USA)
[49]  H.K.Pathak, P. Singh, A New Bandwidth Interval Based Forecasting Method for Enrollments Using Fuzzy Time Series, Applied Mathematics, Vol. 2, No. 4 (2011), PP.504-507, DOI: 10.4236/am.2011.24065 (USA)

Publications: Books/Book Chapters

[1]  Discrete Mathematics (Hindi/English), 10th ed. 2001-02, Shiksha Sahitya Prakashan , Meerut , India.
[2]  Abstract Algebra (Hindi/English), 8th ed. 2001-02, Shiksha Sahitya Prakashan , Meerut , India.
[3]  Differential Equations and Fourier Series (Hindi/English), 3rd ed. 2001-02, Shiksha Sahitya Prak., Meerut , India
[4]  Analytical Geometry and Differential Equations (Hindi/English), Shiksha Sahitya Prakashan, Meerut , India
[5]  Mathematical Analysis, Shiksha Sahitya Prakashan , Meerut , India.
[6]  Algebra & Trigonometry (Hindi/English), Shiksha Sahitya Prakashan , Meerut , India, 2002 (UGC-Syllabus).
[7]  Calculus (Hindi/English), Shiksha Sahitya Prakashan , Meerut , India, 2002 (UGC-Syllabus).
[8]  Vector Analysis and Geometry (Hindi/English), 2002 (UGC-Syllabus), Shiksha Sahit. Prak. , Meerut , India.
[9]  Advanced Calculus (Hindi/English), 2003 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut , India.
[10]  Differential Equations (Hindi/English), 2003 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut , India.
[11]  Mechanics (Hindi/English), 2003 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut , India.
[12]  Linear Algebra (Hindi/English), Shiksha Sahitya Prakashan , Meerut , India
[13]  Analysis (Hindi/English), 2003 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut , India
[14]  Statistical Method (Hindi/English), Shiksha Sahitya Prakashan , Meerut , India
[15]  Numerical Analysis (Hindi), Shiksha Sahitya Prakashan , Meerut , India
[16]  Modern Algebra, Shiksha Sahitya Prakashan , Meerut , India
[17]  Real Analysis, 2003 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut , India
[18]  Complex Analysis, 2003 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut , India
[19]  Functional Analysis, 2001, Shiksha Sahitya Prakashan , Meerut , India
[20]  Operations Research , 2003 (UGC-Syllabus), Shiksha Sahitya Prakashan, Meerut , India
[21]  Topology, 2003 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut, India.
[22]  Abstract Algebra, 2004 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut, India.
[23]  Advanced Abstract Algebra, 2007 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut, India
[24]  Advanced Discrete Mathematics , 2007 (UGC-Syllabus), Shiksha Sahitya Prakashan , Meerut , India.
[25]  Applied Engineering Mathematics ( Sem. I), 2006, Shiksha Sahitya Prakashan , Meerut , India.
[26]  Applied Engineering Mathematics (Sem. II), 2005, Shiksha Sahitya Prakashan , Meerut , India.
[27]  Applied Engineering Mathematics (Sem. III), 2007, Shiksha Sahitya Prakashan , Meerut , India.
[28]  Discrete Mathematical Structure (Sem. IV), 2008, Shiksha Sahitya Prakashan , Meerut , India.
[29]  Engineering Mathematics ( Sem. I), 2008, Shiksha Sahitya Prakashan , Meerut , India.
[30]  Engineering Mathematics ( Sem. II), 2009, Shiksha Sahitya Prakashan , Meerut , India.
[31]  Engineering Mathematics ( Sem. III), 2008, Shiksha Sahitya Prakashan , Meerut , India.
[32]  Discrete Structure ( Sem. IV), 2009, Shiksha Sahitya Prakashan , Meerut , India.
[33]  Matrices, Theory of Equations and Trigonometry (Sem. I) (Hindi/English), 2008, Shik. Sahit. Prak. , Meerut , India.
[34]  Calculus (Sem. I) (Hindi/English), 2008, Shiksha Sahitya Prakashan , Meerut , India.
[35]  Vector (Sem. I) (Hindi/English), 2008, Shiksha Sahitya Prakashan , Meerut , India.
[36]  Elementary Abstract Algebra (Sem. II) (Hindi/English), 2009, Shiksha Sahitya Prakashan , Meerut , India.
[37]  Differential Equations-I (Sem. II) ) (Hindi/English), 2009, Shiksha Sahitya Prakashan , Meerut , India.
[38]  Vector Analysis and Vector Calculus (Sem. II) ) (Hindi/English), 2009, Shiksha Sahitya Prakash. , Meerut , India.
[39]  Advanced Calculus –Part I (Sem. III) (Hindi/English), 2009, Shiksha Sahitya Prakashan , Meerut , India.
[40]  Differential Equations-Part II (Sem. III) ) (Hindi/English), 2009, Shiksha Sahitya Prakashan , Meerut , India.
[41]  Mechanics-Part I (Sem. III) ) (Hindi/English), 2009, Shiksha Sahitya Prakashan , Meerut , India
[42]  Advanced Calculus –Part II (Sem. IV) (Hindi/English), 2009, Shiksha Sahitya Prakashan , Meerut , India
[43]  Differential Equations &Calculus of Variation (Sem. IV ) (Hindi/English), 2009, Shiksha Sahitya Prakashan , Meerut , India.
[44]  Mechanics-Part II (Sem. IV) ) (Hindi/English), 2009, Shiksha Sahitya Prakashan , Meerut , India
[45]  Discrete Mathematics (B.C.A.-101), 2nd ed. 2008-09, Shiksha Sahitya Prakashan , Meerut , India.
[46]  Calculus & Statistical Analysis (B.C.A.-101), 2nd ed. 2008-09, Shiksha Sahitya Prakashan , Meerut , India.
[47]  Differentiation and Integration (B.C.A.-201), 1st ed. 2008-09, Shiksha Sahitya Prak., Meerut , India
[48]  Numerical Analysis (B.C.A.-201), 1st ed. 2008-09, Shiksha Sahitya Prak., Meerut , India
[49]  Differential Equations and Fourier Series (B.C.A.-301), 1st ed. 2008-09, Shiksha Sahitya Prak., Meerut , India
[50]  Calculus and Geometry (B.C.A.-301), 1st ed. 2008-09, Shiksha Sahitya Prak., Meerut , India
[51]  Numerical Analysis (Sem III), 2009, Shiksha Sahitya Prakashan , Meerut , India.