Banach’s Contraction Principle for Nonlinear Contraction Mappings in Modular Metric Spaces
Sign Up to like & getrecommendations! Published in 2017 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-016-0387-2
Abstract: The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate some fixed-point theorems… read more here.
Keywords: modular metric; banach contraction; metric spaces; principle nonlinear ... See more keywords
Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces
Sign Up to like & getrecommendations! Published in 2021 at "Arab Journal of Mathematical Sciences"
DOI: 10.1108/ajms-10-2020-0098
Abstract: The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The… read more here.
Keywords: fixed point; metric spaces; integral equations; solving nonlinear ... See more keywords
Fixed Point Results on Partial Modular Metric Space
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DOI: 10.3390/axioms11020062
Abstract: In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality. In support of this,… read more here.
Keywords: metric space; partial modular; modular metric; fixed point ... See more keywords
Fixed Point Results in Modular b-Metric-like Spaces with an Application
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DOI: 10.3390/axioms13100726
Abstract: In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of ξ-convergence, ξ-Cauchy sequence, ξ-completeness and ξ-contraction. The existence and uniqueness… read more here.
Keywords: like spaces; fixed point; metric like; modular metric ... See more keywords
Non-Unique Fixed Point Theorems in Modular Metric Spaces
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DOI: 10.3390/sym11040549
Abstract: This paper is devoted to the study of Ćirić-type non-unique fixed point results in modular metric spaces. We obtain various theorems about a fixed point and periodic points for a self-map on modular spaces which… read more here.
Keywords: fixed point; metric spaces; unique fixed; non unique ... See more keywords
On Modular b-Metrics
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DOI: 10.3390/sym16101333
Abstract: The notions of modular b-metric and modular b-metric space were introduced by Ege and Alaca as natural generalizations of the well-known and featured concepts of modular metric and modular metric space presented and discussed by… read more here.
Keywords: modular metric; topology; class; modular metrics ... See more keywords
On the modular metric completion
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DOI: 10.4995/agt.2025.23431
Abstract: The purpose of this paper is to present the construction of the completion of a set equipped with a modular metric that we call the modular completion. We show for instance that any set equipped… read more here.
Keywords: metric completion; completion; modular completion; modular metric ... See more keywords