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In this paper, we  introduce and study a new iterative method which is based on viscosity general algorithm and forward-backward splitting method  for finding a common element of the set of common fixed points of multivalued demicontractive and quasi-nonexpansive mappings and the set of solutions of  variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings in  real Hilbert spaces. We prove that the sequence $x_n$ which is generated by the proposed iterative algorithm converges strongly to a common element of two sets above. Finally, our theorems are applied to approximate a common solution of fixed point problems with set-valued operators and the composite convex minimization problem. Our theorems are significant improvements on several important recent results.

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In this paper, we prove some coupled fixed point theorems for nonlinear contractive mappings which doesn't have the mixed monotone property, in the context of partially ordered `G`-metric spaces. Hence, these results can be applied in a much wider class of problems. Our results improve the result of D. Dori'{c}, Z. Kadelburg and S. Radenovi'{c} [Appl. Math. Lett. (2012)]. We also present two examples to support these new results.

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In this work, the common T approximate strict fixed point property for multi-valued mappings F,G : X -> P_{cl,bd}(X) is introduced to prove necessary and sufficient condition for existence of a common strict xed point of multi-valued mappings involved therein. Our results extend and unify comparable results in the existing literature. We also provide examples to support our results.

 

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We introduce variational inequality problems on 2-inner product spaces and prove several existence results for variational inequalities defined on closed convex sets. Also, the relation between variational inequality problems, best approximation problems and fixed point theory is studied.

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In this article,  two new fixed point results in the framework of complex-valued rectangular extended $b$-metric space are established. Our results include as special cases, some well-known results in the comparable literature.  We provide nontrivial examples and an existence theorem of  a Fredholm type integral equation to support our assertions and to indicate a usability of the results presented herein.

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The definition of bipolar multiplicative metric space is introduced in this article, and in this space some properties are derived. Multiplicative contractions for covariant and contravariant maps are defined and fixed points are obtained. Also, some fixed point results of covariant and contravariant maps satisfying multiplicative contraction conditions are proved for bipolar multiplicative metric spaces. Moreover, Banach contraction principle and Kannan fixed point theorem are generalized.

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Common fixed point theorems for three self mappings satisfying generalized contractive conditions in cone metric spaces are derived. Also, some common fixed point results for two self mappings are deduced. Moreover, these all results generalize some important familiar results. Given example to illustrate our main result. Furthermore, an existence theorem for the common solution of the two Urysohn integral equations obtained by using our main result.

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In this article, we proposed a modified implicit iterative algorithm for approximation of common fixed point of finite families of two uniformly L-Lipschitzian total asymptotically pseudocontractive mappings in Banach spaces. Our new iterative algorithm contains some well known iterative algorithm which has been used by several authors for approximating fixed
points of different classes of mappings. We prove some convergence theorems of our new iterative method and validate our main result with a numerical ex-
ample. Our result is an improvement and generalization of the results of some well known authors in the existing literature.

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The aim of this paper is to investigate the existence and uniqueness of solution for a class of nonlinear integro-differential equations known as Hammerstein type. We study fractional equations in the Banach space whose derivative is of the Caputo type. The existence of solution is studied by using the Schauder's fixed point theorem, and the uniqueness is established via a generalization of the Banach fixed point theorem. Finally, an example is given to illustrate the analytical findings.

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We introduce an iterative algorithm for split equality fixed point and null point problem for Lipschitzian quasi-pseudocontractive
mappings and maximal monotone operators which includes split equality feasibility problem, split equality fixed problem, split equality null point
problem and other problem related to fixed point problems. Moreover, we establish a strong convergence results in real Hilbert spaces under
some suitable conditions and reduce our main result to above-mentioned problems. Finally, we apply the study to split equality feasibility problem (SEFP), split equality equilibrium problem (SEEP), split equality variational inequality problem (SEVIP) and split equality optimization problem (SEOP). The results presented in the paper extend and improve many recent results.