On Quadruple Random Fixed Point Theorems in Partially Ordered Metric Spaces

Bhaskar and Lakshmikantham in [15] introduced the concept of coupled fixed point of a mapping and investigated the existence and uniquencess of a coupled fixed point theorem in partially ordered complete metric space. Lakshmikantham and Ciric [16] defined  mixed g-monotone property and coincidence point in partially ordered metric space. V. Berinde and M. Borcut[18] introduced the concept of triple fixed point and proved some related theorems. Following this trand,  Karapinar[19] introduced the nation of quadruple fixed point. The object of this note is to prove quadruple random fixed point theorem in partially ordered metric spaces.

[1]  V. Lakshmikantham,et al.  Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces , 2009 .

[2]  C. J. Himmelberg,et al.  On measurable relations , 1982 .

[3]  Erdal Karapinar,et al.  Computers and Mathematics with Applications Quadruple Fixed Point Theorems for Nonlinear Contractions , 2022 .

[4]  Erdal Karapinar,et al.  QUADRUPLE FIXED POINT THEOREMS FOR NONLINEAR CONTRACTIONS IN PARTIALLY ORDERED METRIC SPACES , 2012 .

[5]  Ismat Beg,et al.  RANDOM FIXED POINT THEOREMS FOR NONEXPANSIVE AND CONTRACTIVE-TYPE RANDOM OPERATORS ON BANACH SPACES , 1994 .

[6]  Hong-Kun Xu,et al.  Some random fixed point theorems for condensing and nonexpansive operators , 1990 .

[7]  A. T. Bharucha-Reid,et al.  Fixed point theorems in probabilistic analysis , 1976 .

[8]  Shigeru Itoh,et al.  Random fixed point theorems with an application to random differential equations in Banach spaces , 1979 .

[9]  V. Lakshmikantham,et al.  Fixed point theorems in partially ordered metric spaces and applications , 2006 .

[10]  R. Rockafellar.  Measurable dependence of convex sets and functions on parameters , 1969 .

[11]  Erdal Karapinar.  Quartet fixed point for nonlinear contraction , 2011 .

[12]  Hassen Aydi,et al.  Mixed g-monotone property and quadruple fixed point theorems in partially ordered metric spaces , 2012 .

[13]  Vasile Berinde,et al.  Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces , 2011 .

[14]  A. Ran,et al.  A fixed point theorem in partially ordered sets and some applications to matrix equations , 2003 .

[15]  Erdal Karapinar,et al.  Quadruple Fixed Point Theorems under Nonlinear Contractive Conditions in Partially Ordered Metric Spaces , 2012, J. Appl. Math..

[16]  O. Hanš.  Random Operator Equations , 1961 .

[17]  Mihai Turinici,et al.  Abstract comparison principles and multivariable Gronwall-Bellman inequalities , 1986 .

[18]  Syed Abdul Mohiuddine,et al.  On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces , 2012 .

[19]  Nikolaos S. Papageorgiou.  Random fixed point theorems for measurable multifunctions in Banach spaces , 1986 .

[20]  E. J. McShane,et al.  On Filippov’s implicit functions lemma , 1967 .

[21]  Shigeru Itoh.  A Random Fixed Point Theorem for a Multivalued Contraction Mapping , 1976 .

[22]  Daniel H. Wagner.  Survey of Measurable Selection Theorems , 1977 .