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Content available remote The N-fuzzy metric spaces and mappings with application
In the present paper, we introduce the notion of N-fuzzy metric spaces (NFMSs), Pseudo N-fuzzy metric spaces and describe some of their properties. Also we prove a fixed point theorem using implicit relation in N-fuzzy metric spaces.
In the present paper, we extend the concept of Weak Reciprocal Continuity for a hybrid pair of single-valued and multi-valued maps and introduce (T, f)-completeness of the space. Further, we establish some results on the existence of coincidence and fixed points for the hybrid pair of maps. Our results generalize several well known results available in the literature.
Content available remote Conditional reciprocal continuity and common fixed points
The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of conditional reciprocal continuity. We demonstrate that conditional reciprocal continuity ensures the existence of fixed points under contractive conditions which otherwise do not ensure the existence of fixed points. Our results generalize and extend several well-known fixed point theorems in the setting of metric spaces. We also provide more answers to the open problem posed by B. E. Rhoades [Contractive Definitions and Continuity, Contemporary Math. 72 (1988), 233-245] regarding existence of a contractive condition which is strong enough to generate a fixed point, but which does not force the map to be continuous at the fixed point.
In this paper, we prove some fixed point theorems for two hybrid pairs of mappings in 2-metric spaces by using some weaker conditions.
In the present paper, we extend and generalize the result of Cho et. al. [l]by introducing the notion of weakly L-compatible and weakly M-compatible maps in a 2 non-Archimedean Menger PM-space.
Content available remote (ε, δ) contractive condition and common fixed points
In the present paper we prove a common fixed point theorem (Theorem 1) for four mappings under the (ε, δ) contractive condition, however, without either imposing any additional restriction on δ or assuming the ∅-contractive condition together with. While proving the theorem, neither the completeness of the metric space is assumed nor any of the mappings is required to be continuous. Thus we also provide one more answer to the problem of Rhoades [24] which ensures the existence of common fixed point, however, does not force the maps to be continuous at the common fixed point. Theorem 2 generalizes further the result obtained in Theorem 1.
Content available remote A common fixed point theorem in non-Archimedean Menger pm-spaces
In the present work, we introduce two types of compatible maps in non-Archimedean Menger PM-spaces and obtain a common fixed point theorem for six maps.
Content available remote Noncommuting maps and invariant approximations
We obtain common fixed point results for generalized I-nonexpansive compatible as well as weakly compatible maps. As applications, various best approximation results for this class of maps are derived in the setup of certain metrizable topological vector spaces.
In this paper, we first formulate the definition of compatible maps and compatible maps of types (alpha) and (beta) in intuitionistic fuzzy metric spaces and give some relations between the concepts of compatible maps and compatible maps of types (alpha) and (beta).
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