DEPARTMENT.FACULTY

photo
Prof. Rais Ahmad
  • DEPARTMENT_STAFF.QUALIFICATION

    Ph.D.

  • DEPARTMENT_STAFF.DESIGNATION

    Professor

  • DEPARTMENT_STAFF.THRUST_AREA

    Nonlinear Analysis and Optimization

  • DEPARTMENT_STAFF.ADDRESS

    T-5 AZIM ESTATE, NEW S.S. NAGAR, ALIGARH-202002, U.P., INDIA

  • DEPARTMENT_STAFF.MOBILE

    9997561075

  • DEPARTMENT_STAFF.EMAIL

    raisain_123@rediffmail.com, pfrais123@gmail.com

  • DEPARTMENT_STAFF.TIME_TABLE

    Time Table

DEPARTMENT_STAFF.COMPLETE_CV
DEPARTMENT_STAFF.PROFILE
1. Research Interest: Variational Inequalities; Fixed Point Theorems; KKM Theory; Nonlinear Functional Analysis and Optimization. 2. Teaching Focus: Calculus; Real Analysis; Measure Theory; Numerical Analysis; Linear Algebra. 3. List of Journals in which my papers are published: Abstract and Applied Analysis; Journal of Optimization Theory and Applications, Journal of Global Optimization; Fuzzy Sets and Systems; Journal of Computational and Applied Mathematics; ANZIAM; Journal of Mathematical Analysis and Applications; Mathematical and Computer Modelling; Computers and Mathematics with Applications; Applied Mathematics and Computation; Bulletin of Australian Mathematical Society; Applied Mathematics Letters; International Journal of Fuzzy Systems; Filomat; Journal of Inequalities and Applications; Fixed Point Theory and Applications; Taiwanese Journal of Mathematics; Indian Journal of Pure and Applied Mathematics
  1. Research Paper Publications 2021
    1. Generalized complementarity problem with three classes of generalized variational inequalities involving XOR-operator, Journal of Mathematics, Volume 2021, Article ID 6629203, 10 pages (2021) (with I. Ahmad, Z.A. Rather and Y. Wang). 

  2. Research Paper Publications 2020
    1. Sensitivity Analysis of Mixed Cayley Inclusion Problem with XOR-operation, Symmetry, Vol. 12, 220, 2020 (with I. Ali, M. Ishtyak and C.-F. Wen). 
    2. Cayley inclusion problem with its corresponding generalized resolvent equation problem in uniformly smooth Banach spaces, Applicable Analysis, 2020 (With M. Ishtyak, I. Ali, M. Rahaman and J.C. Yao). 
    3. System of random variational inclusions involving random fuzzy mappings with XOR-operation, Journal of Nonlinear and Convex Analysis, Vol.21(10), pp. 2257-2271 (2020) (with Z.A. Rather, H.A. Rizvi and M.-M. Wong). 

  3. Research Paper Publications 2019
    1. Existence results of the system of generalized variational inequalities with multi-valued mappings, RACSAM, Vol. 113, No. 1, pp. 119-129 (2019) (with M. Rahaman, J. Iqbal and Priyanka Gupta) (ISSN: 1579-1505, IF: 0.691). 
    2. The Yosida approximation iterative technique for split monotone Yosida variational inclusions, Numerical Algorithm, 2019 (With M. Rahaman, M. Ishtyak and I. Ali), (ISSN: 1572-9265) 
    3. Cayley Inclusion Problem Involving XOR-operation, Mathematics, Vol. 7(3), 302, 2019 (with I. Ali and C.-F. Wen)

    4. Generalized Nonsmooth Exponential-Type Vector Variational-Like Inequalities and Nonsmooth Vector Optimization Problems in Asplund Spaces, Mathematics, Vol. 7(4), 345, 2019 (with S.S. Irfan, M. Rahaman, I. Ahmad and S. Hussain)

    5. Generalized Implicit Set-Valued Variational Inclusion Problem with ? Operation, Mathematics), Vol. 7(5), 421, 2019 (with I. Ali, S. Husain, A. Latif and C.F. Wen)

    6. Convergence analysis and stability of perturbed three-step iterative algorithm for generalized mixed ordered quasi-variational inclusion involving XOR operator, Optimization, https://doi.org/10.1080/02331934.2019.1652910, 2019 (with I. Ahmad, M. Rahaman and I. Ali)

    7. System of multi-valued mixed variational inclusions with XOR-operation in real ordered uniformly smooth Banach Spaces, Mathematics, Vol. 7(11), 1027, 2019 (with I. Ali, X.-B. Li, M. Ishtyak and C.F. Wen).

  4. Research Paper Publications 2018
    1. Co-proximal operators for solving generalized co-variational inclusion problems in q-uniformly smooth Banach spaces, Journal of Nonlinear Convex Analysis, Vol. 19(7), pp. 1093-1107, 2018 (with S.S. Irfan, I. Ahmad and M. Rahaman) (ISSN: 1880-5221, IF: 0.691). 
    2. H(·, ·)-ordered-compression mapping for solving XOR-variational inclusion problem, Journal of Nonlinear and Convex Analysis, Vol. 19(12), pp. 2189- 2201, 2018 (With I. Ahmad, I. Ali, S. Al-Homidan and Y.H. Wang), (ISSN: 1880-5221, IF: 0.691)
  5. Research Paper Publications 2017
    1. Auxiliary principle technique and iterative algorithm for a new system of generalized multi-valued mixed quasi equilibrium-like problem, Journal of Inequalities and Applications, (2017) 2017:56 DOI 10.1186/s13660-017-1324-0 (With M. Rahaman, C.T. Pang and M. Ishtyak) (IF: 0.630) 
    2. System of Yosida inclusion involving XOR operator, Journal of Nonlinear Convex Analysis, Vol. 18(2), pp. 831-845, 2017 (with I. Ahmad, C.T. Pang and M. Ishtyak) (ISSN: 1880-5221, IF: 0.691). 
  6. Research Paper Publications 2016
    1. Mixed vector equilibrium problem involving multi-valued mappings, Applied Mathematics and Information Sciences, Vol. 10, No. 1, 203-207 (2016) (with M. Rahaman and Adem Kilicman). (ISSN: 2325-0399, IF: 1.232) 
    2. Convergence theorems for split equality generalized mixed equilibrium problems for demi-contractive mappings, Journal of Inequalities and Applications, 2015:418, doi:10.1186/s13660-015-0936-5 (with M. Rahaman, YC Liou and I Ahmad). (IF: 0.77) 
    3. An iterative algorithm for a system of generalized implicit variational inclusions, SpringerPlus, Vol. 5: 1283. DOI: 10.1186/s40064-016-2916-8 (2016) (with V.N. Mishra, I. Ahmad and M. Rahaman). (IF:0.982) 
    4. Common solutions for a system of generalized unrelated variational inequalities, Maejo International Journal of Science and Technology, Vol. 10, No. 03, 354-362 (2016) (with H.A. Rizvi and V.N. Mishra), (ISSN: 1905-7873, IF: 0.367) 
  7. Research Paper Publications 2015
    1. Graph convergence for the H(·, ·)-co-accretive mapping with an application, Bulletin of Malaysian Mathematical Sciences Society, Vol. 38, No. 4, pp. 1481- 1506 (2015) (with M. Akram and M. Dilshad). (ISSN: 0126-6705, IF:0.798) 
    2. Generalized vector complementarity problem with fuzzy mappings, Fuzzy Sets and Systems, Vol. 280, 133-141, DOI: 10.1016/j.fss.2015.01.008 (2015) (with A. K?l?çman and M. Rahaman). (ISSN: 0165-0114, IF:1.88) 
    3. Fuzzy resolvent equation with H(·, ·)-?-?-accretive operator in Banach spaces, Iranian Journal of Fuzzy Systems, Vol. 12, Issue 2, pp. 95-106, 2015 (with M. Dilshad). (ISSN: 1735-0654, IF: 1.06) 
    4. Generalized strongly vector equilibrium problem for set-valued mappings, Filomat, Vol. 28, No. 9, pp. 1783-1790, 2015 (M. Rahaman). (ISSN: 2406-0933, IF: 0.753) 
    5. Fuzzy vector equilibrium problem, Iranian Journal of Fuzzy Systems, Vol. 12, Issue 1, pp. 115-122, 2015 (with M. Rahaman). (ISSN: 1735-0654, IF: 1.06) 
    6. Some existence results for generalized vector quasi-equilibrium problem, Bulletin of the Iranian Mathematical Society, Vol. 41, No. 6, 1413-1422 (2015) (with M. Akram). (ISSN: 1017-060X, IF: 0.27) 
    7. Relaxed ?-proximal operator for solving a variational-like inclusion problem, Mathematical Modelling and Analysis, Vol. 20, No. 6, 2015, 819-835 DOI: 10.3846/13926292.2015.1117026(with M. Rahaman, M. Dilshad and I. Ahmad) (Impact factor: 0.83, ISSN: 1648-3510). 

  8. Research Paper Publications 2014
    1. Extended mixed vector equilibrium problems, Abstract and Applied Analysis, Vol. 2014, Article ID 376759, 6 Pages, doi:10.1155/ 2014/376759, (with M. Rahaman and A. K?l?çman). (ISSN:1085-3375, IF:1.274) 
    2. Existence results for strong mixed vector equilibrium problem for multivalued mappings, Abstract and Applied Analysis, Vol. 2014, Article ID 497846, 6 Pages, doi:10.1155/2014/497846, (with M. Rahaman and A. K?l?çman). (ISSN:1085-3375, IF:1.274) 
    3. Generalized equilibrium problem with mixed relaxed monotonicity, The Scientific World Journal, Vol. 2014, Article ID 807324, 4 Pages, doi:10.1155/ 2014/807324, (with H.A. Rizvi and A. K?l?çman). (ISSN:2356-6140, IF:1.219) 

  9. Research Paper Publications 2013
    1. Generalized monotone mapping with an application for solving a variational inclusion problem, J. Optim. Theory Appl., Vol. 157, No. 2, pp. 324-346 (2013)(with M. Akram and J.C. Yao). (ISSN: 0022-3239, IF: 1.423) 
    2. Korovkin type approximation theorem through statistical lacunary summability, Iranian Journal of Science and Technology - Transaction A2, pp. 99-102 (2013) (with Mursaleen). (ISSN:1028-6276, IF:0.03) 
    3. A system of generalized resolvent equations involving generalized pseudocontractive mapping, Iranian Journal of Science and Technology-Transaction A, Vol. 37, Issue 3.1 (Special Issue) (2013), pp. 431-438. (with M. Akram). (ISSN:1028-6276, IF:0.03) 
  10. Research Paper Publications 2012
    1. System of generalized H-resolvent equations with corresponding system of generalized variational inclusions, Hacettepe Journal of Mathematics and Statistics, Vol. 41(1), 33-45 (2012) (with Mursaleen). (ISSN:1303-1510, IF:0.212) 
    2. Generalized set-valued variational like inclusion involving H(., .) ? ?- cocoercive operators in Banach space, Journal of Inequalities and Applications, (with M. Dilshad, M.M. Wong and J. C. Yao), doi: 10.1186/1029-242X-2012- 149 (2012). (ISSN:1025-5834, IF:0.73) 
    3. H(·, ·)-?-cocoercive operators and variational-like inclusions in Banach space, J. Nonlinear Sci. Appl., Vol. 5, pp. 334-344 (2012). (with M. Dilshad). (ISSN 2008-1901) 
    4. Resolvent operator technique for solving a system of generalized variational -like inclusions in Banach spaces, Filomat, Vol. 26, No. 5, pp. 897-908 (2012) (with M. Dilshad and M. Akram). (ISSN 0354-5180, IF:0.101) 
    5. On completely generalized multi-valued co-variational inequalities involving strongly accretive operators, Filomat, Vol. 26, No. 4, pp. 657-663 (2012) (with S. S. Irfan). (ISSN 0354-5180, IF:0.101) 
    6. Mixed variational inclusions involving infinite family of fuzzy mappings, Iranian Journal of Fuzzy Systems, Vol. 9, No. 5, pp. 125-135 (2012) (with M. Dilshad, J. C. Yao). (ISSN:1735-0654, IF: 1.06) 
  11. Research Paper Publications 2011
    1. Variational-like inclusions and resolvent equations involving infinite family of set-valued mappings, Fixed point theory and applications, Vol. 2011, Article ID 261534, 12 Pages, doi:10.1155/2011/635030, (with M. Dilshad). (ISSN:1687-1820, IF:1.525) 
    2. H(·, ·)-cocoercive operator and an application for solving generalized variational inclusions, Abstract and Applied Analysis, Vol. 2011, Article ID 635030, 13 Pages, doi:10.1155/2011/261534, (with M. Dilshad, M.M. Wong and J.C. Yao). (ISSN:1085-3375, IF:1.442) 
  12. Research Paper Publications 2010
    1. Generalized multivalued vector variational-like inequalities, Journal of global optimization, 46, 25-30 (2010) (with S.S. Irfan). (ISSN: 0925-5001, IF:1.454) 

LISTDownloadUPLOADED DATE
Aims and Objectives of Measure Theory
20/11/2021
Syllabus(Measure Theory)
20/11/2021
Unit-I (Measure Theory)
20/11/2021
Unit-II (Measure Theory)
20/11/2021
Unit-III (Measure Theory)
20/11/2021
Unit-IV (Measure Theory)
20/11/2021