TY - JOUR
T1 - Banach Contraction Principle-Type Results for Some Enriched Mappings in Modular Function Spaces
AU - Khan, Safeer H
AU - Al-Mazrooei, Abdullah Eqal
AU - Latif, Abdul
PY - 2023/6/1
Y1 - 2023/6/1
N2 - The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study of enriched mappings in modular function spaces. We first introduce the concepts of enriched (Formula presented.) -contractions and enriched (Formula presented.) -Kannan mappings in modular function spaces. We then establish some Banach Contraction Principle type theorems for the existence of fixed points of such mappings in this setting. Our results for enriched (Formula presented.) -contractions are generalizations of the corresponding results from Banach spaces to modular function spaces and those from contractions to enriched (Formula presented.) -contractions. We make a first ever attempt to prove existence results for enriched (Formula presented.) -Kannan mappings and deduce the result for (Formula presented.) -Kannan mappings. Note that even (Formula presented.) -Kannan mappings in modular function spaces have not been considered yet. We validate our main results by examples.
AB - The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study of enriched mappings in modular function spaces. We first introduce the concepts of enriched (Formula presented.) -contractions and enriched (Formula presented.) -Kannan mappings in modular function spaces. We then establish some Banach Contraction Principle type theorems for the existence of fixed points of such mappings in this setting. Our results for enriched (Formula presented.) -contractions are generalizations of the corresponding results from Banach spaces to modular function spaces and those from contractions to enriched (Formula presented.) -contractions. We make a first ever attempt to prove existence results for enriched (Formula presented.) -Kannan mappings and deduce the result for (Formula presented.) -Kannan mappings. Note that even (Formula presented.) -Kannan mappings in modular function spaces have not been considered yet. We validate our main results by examples.
KW - enriched ρ-contraction
KW - enriched ρ-Kannan mapping
KW - fixed point
KW - iterative process
KW - modular function space
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85163623830&origin=inward
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U2 - 10.3390/axioms12060549
DO - 10.3390/axioms12060549
M3 - Article
SN - 2075-1680
VL - 12
JO - Axioms
JF - Axioms
IS - 6
M1 - 549
ER -