Some fixed point results for generalized contraction mappings with cyclic ( α , β ) -admissible mapping in multiplicative metric spaces

Abstract

The purpose of this work is to introduce new types of contraction mappings in the sense of a multiplicative metric space. Fixed point results for these contraction mappings in multiplicative metric spaces are obtained. Our presented results generalize, extend, and improve results on the topic in the literature. Moreover, our results cannot be directly obtained as a consequence from the corresponding results in metric spaces. We also state some illustrative examples to claim that our results properly generalize some results in the literature. We apply our main results for proving a fixed point theorem involving a cyclic mapping. MSC: 47H09; 47H10

Best Proximity for Two Pairs of Mappings in Multiplicative Metric Space

“…They established several xed point theorems in full multiplicative metric space, which laid the foundation for the idea of multiplicative contraction mapping. Please see [7,12,13,17,20] for further ndings on multiplicative metric space. ( [3-5, 7, 9-11, 15, 16, 18, 19, 21] and references therein) has applications for multiplicative calculus.…”

“…Dnition 1.10. [17] Let A and B be nonempty subsets of a multiplicative metric space (X, d). A mapping T : A → B is said to be proximal contraction if there exists a nonnegative α ∈ [0, 1) such that, for all u, v, x, y in A, It can be observed that a best proximity point reduces to a xed point if the underlying mapping is a self-mapping.…”

Existence of Common Coupled Fixed Points of Generalized Contractive Mappings in Ordered Multiplicative Metric Spaces

“…Hxiaoju et al [24] studied common fixed points for weak commutative mappings on a multiplicative metric space (see also, [25]). Recently, Yamaod and Sintunavarat [26] obtained some fixed point results for generalized contraction mappings with cyclic (α, β)-admissible mapping in multiplicative metric spaces. In this paper, unique common coupled fixed point results for w * − compatible maps, which are more general than commuting and w− compatible mappings, are obtained in partially ordered multiplicative metric spaces, without exploiting the notion of continuity.…”

Coupled Fixed Point Theorems in Partially Ordered Multiplicative Metric Space and Its Applications

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