Abstract
In this paper, we introduce a new concept of generalized cyclic (κh, ϕL)S-weak contraction mappings and establish some coincidence point results for such mappings in complete partially ordered Menger PM-spaces. Our results generalize the main results of Nashine (Nonlinear Anal. 75:6160-6169, 2012) and Gopal et al. (Appl. Math. Comput. 233:955-967, 2014). We also obtain the corresponding coincidence point theorems for generalized cyclic (κh, ϕL)S-weak contractions in partially ordered metric spaces. MSC: 47H10; 54H25
Highlights
Introduction and preliminariesFixed point theory is a very useful tool in many fields such as nonlinear operator theory, control theory, game theory, dynamics and economic theory
In, Harjani and Sadarangani [ ] proved some fixed point theorems for weakly contractive mappings in complete metric spaces endowed with a partial order
We introduce the notion of generalized cyclicS-weak contraction mappings to establish some corresponding coincidence point theorems in complete partially ordered Menger PM-spaces
Summary
→Y be two self-maps. Then is said to be a cyclic representation of Y with respect to S and T, if the following two conditions are satisfied: (i) S(Ai), i = , , . . . , m, are nonempty closed sets; (ii) T(A ) ⊆ S(A ), T(A ) ⊆ S(A ), . . . , T(Am) ⊆ S(A ). Example . Ai.
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