<i>C</i>*-Algebra-Valued Partial Modular Metric Spaces and Some Fixed Point Results
Santanu Narzary,
Dipankar Das,
Yumnam Mahendra Singh,
Mohammad Saeed Khan,
Salvatore Sessa
Affiliations
Santanu Narzary
Department of Mathematical Sciences, Bodoland University, Kokrajhar 783370, Assam, India
Dipankar Das
Department of Mathematical Sciences, Bodoland University, Kokrajhar 783370, Assam, India
Yumnam Mahendra Singh
Department of Humanities and Basic Sciences, Manipur Institute of Technology, A Constitute College of Manipur University, Takyepat 795004, Manipur, India
Mohammad Saeed Khan
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Gauteng 0208, South Africa
Salvatore Sessa
Department of Architecture, Federico II Naples University, Via Toledo 402, 80134 Naples, Italy
In the present paper, we introduce the notion of C*-algebra-valued partial modular metric space satisfying the symmetry property that generalizes partial modular metric space, C*-algebra-valued partial metric space, and C*-algebra-valued modular metric space and discuss it with examples. Some fixed point results using (ϕ,MF)-contraction mapping are discussed in such space. In addition, we study the stability of obtained results in the spirit of Ulam and Hyers. As an application, we also provide the existence and uniqueness of the solution for a system of Fredholm integral equations.
