On F-Norms of Quasi-Modular Spaces

Fixed point theorems for contraction mappings in modular metric spaces

“…Banach contraction principle has been extended in many different directions, see [2][3][4][5][6][7][8][9][10]. The notion of modular spaces, as a generalize of metric spaces, was introduced by Nakano [11] and was intensively developed by Koshi, Shimogaki, Yamamuro [11][12][13] and others. Further and the most complete development of these theories are due to Luxemburg, Musielak, Orlicz, Mazur, Turpin [14][15][16][17][18] and their collaborators.…”

Fixed Point Theorems for Various Types of Compatible Mappings of Integral Type in Modular Metric Spaces

“…Since its simplicity and usefulness, it has become a very popular tool in solving existence problems in many branches of mathematical analysis. Banach contraction principle has been extended in many different directions; see [6][7][8][9][10][11][12][13][14]. The notion of modular spaces, as a generalization of metric spaces, was introduced by Nakano [14] and was intensively developed by Koshi and Shimogaki [8] Yamamuro [20] and others.…”

Fixed Point Theorems for Kannan Contractions and Weakly Contractive Mappings on a Modular Metric Space Endowed with a Graph

“…The notion of modular spaces was introduce by Nakano [13] and was intensively develop by Koshi and Shimogaki [11], Yamamuro [17] and by Musielak and Orlicz [12]. Recently, Aghanians and Nourozi [2] discuss the existence and uniqueness of the fixed point for Banach and Kannan contraction defined on modular spaces endowed with a graph.…”