%0 Journal Article %T Iterative solution of split equilibrium and fixed point problems in real Hilbert spaces %A Ezeora, J. N. %A Jackreece, P. C. %J Journal of Nonlinear Sciences and Applications %D 2021 %V 14 %N 5 %@ ISSN 2008-1901 %F Ezeora2021 %X In this article, we introduce a hybrid iteration involving inertial-term for split equilibrium problem and fixed point for a finite family of asymptotically strictly pseudocontractive mappings. We prove that the sequence converges strongly to a solution of split equilibrium problem and a common fixed point of a finite family of asymptotically strictly pseudocontractive mappings. The results proved extend and improve recent results of Chang et al. [S. S. Chang, H. W. J. Lee, C. K. Chan, L. Wang, L. J. Qin, Appl. Math. Comput., \(\bf 219\) (2013), 10416--10424], Dewangan et al. [R. Dewangan, B. S. Thakur, M. Postolache, J. Inequal. Appl., \(\bf 2014\) (2014), 11 pages], and many others. %9 journal article %R 10.22436/jnsa.014.05.06 %U http://dx.doi.org/10.22436/jnsa.014.05.06 %P 359--371 %0 Journal Article %T Approximating fixed points of total asymptotically nonexpansive mappings %A Y. I. Alber %A C. E. Chidume %A H. Zegeye %J Fixed Point Theory Appl. %D 2006 %V 2006 %F Alber2006 %0 Journal Article %T A hybrid extragradient method extended to fixed point problems and equilibrium problems %A P. N. Anh %J Optimization %D 2013 %V 62 %F Anh2013 %0 Journal Article %T Three generalizations of firmly nonexpansive mappings: their relations and continuity properties %A K. Aoyama %A F. Kohsaka %A W. Takahashi %J J. Nonlinear Convex Anal. %D 2009 %V 10 %F Aoyama2009 %0 Journal Article %T Approximation results for split equilibrium problems and fixed point problems of nonexpansive semigroup in Hilbert spaces %A Y. Arfat %A P. Kumam %A P. Sa Ngiamsunthorn %A M. A. A. Khan %A H. Sarwar %A H. Fukhar-ud-Din %J Adv. Difference Equ. %D 2020 %V 2020 %F Arfat2020 %0 Journal Article %T A fast iterative shrinkage-thresholding algorithm for linear inverse problems %A A. Beck %A M. Teboulle %J SIAM J. Imaging Sci. %D 2009 %V 2 %F Beck2009 %0 Journal Article %T From optimization and variational inequalities to equilibrium problems %A E. Blum %A W. Oettli %J Math. Student. %D 1994 %V 63 %F Blum1994 %0 Journal Article %T Construction of fixed points of nonlinear mappings in Hilbert space %A F. E. Browder %A W. V. Petryshyn %J J. Math. Anal. Appl. %D 1967 %V 20 %F Browder1967 %0 Journal Article %T Iterative oblique projection onto convex subsets and the split feasibility problems %A C. Byrne %J Inverse Problem %D 2002 %V 18 %F Byrne2002 %0 Journal Article %T A hybrid iterative scheme for mixed equilibrium problems and fixed point problems %A L.-C. Ceng %A J.-C. Yao %J J. Comput. Appl. Math. %D 2008 %V 214 %F Ceng2008 %0 Journal Article %T A unified approach for inversion problems in intensity modulated radiation therapy %A Y. Censor %A T. Bortfeld %A B. Martin %A A. Trofimov %J Phys. Med. Biol. %D 2006 %V 51 %F Censor2006 %0 Journal Article %T A multi-projection algorithm using Bregman projections in a product space %A Y. Censor %A T. Elfving %J Numer. Algorithms %D 1994 %V 8 %F Censor1994 %0 Journal Article %T The multi-set split feasibility problem and its applications %A Y. Censor %A T. Elfving %A N. Kopf %A T. Bortfeld %J Inverse Problem %D 2005 %V 21 %F Censor2005 %0 Journal Article %T Pertured projections and subgradient projections for the multiple-sets split feasibility problem %A Y. Censor %A A. Motov %A A. Segal %J J. Math. Anal. Appl. %D 2007 %V 327 %F Censor2007 %0 Journal Article %T Split feasibility problem for Quasi-nonexpansive multi-valued mappings and total asymptotically strict pseudo contractive mappings %A S. S. Chang %A H. W. J. Lee %A C. K. Chan %A L. Wang %A L. J. Qin %J Appl. Math. Comput. %D 2013 %V 219 %F Chang2013 %0 Book %T Geometric properties of Banach spaces and nonlinear iterations %A C. Chidume %D 2009 %I Springer Verlag Series: Lecture Notes in Mathematics %C Berlin %F Chidume2009 %0 Journal Article %T The convex feasibility problem in image recovery %A P. L. Combettes %J Adv. Imaging Electron Phys. %D 1996 %V 95 %F Combettes1996 %0 Journal Article %T Equilibrium programming in Hilbert spaces %A P. L. Combettes %A S. A. Hirstoaga %J J. Nonlinear Convex Anal. %D 2005 %V 6 %F Combettes2005 %0 Journal Article %T A hybrid iteration for asymptotically strictly pseudocontractive mappings %A R. Dewangan %A B. S. Thakur %A M. Postolache %J J. Inequal. Appl., %D 2014 %V 2014 %F Dewangan2014 %0 Journal Article %T Iterative Solution of Fixed Points Problem, System of Generalized Mixed Equilibrium Problems and Variational Inclusion Problems %A J. N. Ezeora %J Thai J. Math. %D 2014 %V 12 %F Ezeora2014 %0 Journal Article %T Split feasibilty problem for countable family of multi-valued nonlinear mappings %A J. N. Ezeora %A R. C. Ogbonna %J Mathematicki Vesnik %D 2018 %V 70 %F Ezeora2018 %0 Journal Article %T An inertial-like proximal algorithm for equilibrium problems %A D. V. Hieu %J Math. Methods Oper. Res. %D 2018 %V 88 %F Hieu2018 %0 Journal Article %T A new viscosity-type iteration for a finite family of split variational inclusion and fixed point problems between Hilbert and Banach spaces %A C. Izuchukwu %A F. O. Isiogugu %A C. C. Okeke %J J. Inequal. Appl. %D 2019 %V 2019 %F Izuchukwu2019 %0 Journal Article %T A viscosity iterative technique for split variational inclusion and fixed point problems between a Hilbert space and a Banach space %A C. Izuchukwu %A C. C. Okeke %A F. O. Isiogugu %J J. Fixed Point Theory Appl. %D 2018 %V 20 %F Izuchukwu2018 %0 Journal Article %T Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings %A Q. Liu %J Nonlinear Anal. %D 1996 %V 26 %F Liu1996 %0 Journal Article %T New algorithms for the split variational inclusion problems and application to split feasibility problems %A L. V. Long %A D. V. Thong %A V. T. Dung %J Optimization %D 2019 %V 68 %F Long2019 %0 Journal Article %T An algorithm with strong convergence for the split common fixed point problem of total asymptotically strict pseudocontraction mappings, %A Z. Ma %A L. Wang %J J. Inequal. Appl. %D 2015 %V 2015 %F Ma2015 %0 Journal Article %T A note on the multiple-set split feasibility problem in Hilbert spaces %A E. Masad %A S. Reich %J J. Nonlinear Convex Anal. %D 2007 %V 8 %F Masad2007 %0 Journal Article %T Weak convergence theorems for a system of mixed equilibrium problems and nonspreading mappings in a Hilbert space %A S. Plubtieng %A K. Sombut %J J. Inequal. Appl. %D 2010 %V 2010 %F Plubtieng2010 %0 Journal Article %T Some methods of speeding up the convergence of iteration methods %A B. T. Polyak %J Ussr Comput. Math. Math. Phys. %D 1964 %V 4 %F Polyak1964 %0 Journal Article %T Fixed Point Solutions of Generalized Equilibrium Problems for Nonexpansive Mappings %A Y. Shehu %J J. Comput. Appl. Math. %D 2010 %V 234 %F Shehu2010 %0 Journal Article %T Convergence analysis of a general iterative algorithm for finding a common solution of split variational inclusion and optimization problems %A K. Sitthithakerngkiet %A J. Deepho %A J. Martınez-Moreno %A P. Kumam %J Numer. Algorithms %D 2018 %V 79 %F Sitthithakerngkiet2018 %0 Journal Article %T Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space %A S. Takahashi %A W. Takahashi %J Nonlinear Anal. %D 2008 %V 69 %F Takahashi2008 %0 Book %T Convex Functions and Optimization Methods on Riemannian Manifolds %A C. Udriste %D 1994 %I Kluwer Academic Publishers Group %C Dordrecht %F Udriste1994 %0 Journal Article %T Iterative methods for split feasibility problem in infinite dimensional Hilbert spaces %A H.-K. Xu %J Inverse Problems %D 2010 %V 26 %F Xu2010 %0 Journal Article %T Multiple-set split feasibility problems for total asymp-totically strict pseudocontractions mappings %A L. Yang %A S.-S. Chang %A Y. J. Cho %A J. K. Kim %J Fixed Point Theory Appl. %D 2011 %V 2011 %F Yang2011 %0 Journal Article %T A self-adaptive iterative algorithm for the split common fixed point problems %A J. Zhao %A D. Hou %J Numer. Algorithms %D 2019 %V 82 %F Zhao2019