Coincidence fixed point theorem in a Menger probabilistic metric spaces

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DOI:

https://doi.org/10.26637/MJM0603/0007

Abstract

In this paper, we discuss the existence and uniqueness of solutions for a class of multi-term time-fractional impulsive integro-differential equations with state dependent delay subject to some fractional order integral boundary conditions. In our consideration, we apply the Banach, and Sadovskii fixed point theorems to obtain our main results under some appropriate assumptions. An example is given at the end to illustrate the applications of the established results. Fixed point theory of nonexpansive type single valued mappings provides techniques for solving a variety of applied problems in mathematical sciences and engineering. The aim of this paper is to prove the existence of coincidence points, coupled points and common coupled fixed points of nonexpansive type conditions satisfied by single valued maps which include both continuous and discontinuous mappings on Menger probabilistic metric spaces.

Keywords:

nonexpansive mappings, common fixed point, weak reciprocal continuity, Menger PM space, compatible mappings, common coupled fixed point, coupled point, reciprocal continuity, coincidence point

Mathematics Subject Classification:

Mathematics
  • Pages: 499-505
  • Date Published: 01-07-2018
  • Vol. 6 No. 03 (2018): Malaya Journal of Matematik (MJM)

S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fund. Math., 3(1922) 133-181.

Lj.B. Ć́riríc, On some nonexpansive type mapping and fixed points, Indian J. Pure Appl. Math., 24 (1993) 145 149.

L. Ćirić, RP. Agarwal, B. Samet, Mixed monotonegeneralized contractions in partially ordered probabilistic metric spaces, Fixed Point Theory Appl., 56 (2011).

R. Farokhzad Rostami, common fixed point theorem in a Menger pobabilistic metric spaces, Complex and Nonlinear Systems, 1, N.1 (2017) 11-21.

O. Hadzić, A fixed point theorem in Menger spaces,Publ. Inst. Math. (Belgr.), 20, (1979) 107-112.

RH. Haghi, Sh. Rezapour, N. Shahrzad, some fixed point generalizations are not real generalizations, Nonlinear Anal., 74, (2011) 1799-1803.

O. Hadzić, Z. Ovcin, Fixed point theorems in fuzzy met$left.n, y_nright)$ Tic and probabilistic metric spaces, Zb. Rad. Prir.-Mat. Fak., Ser. Mat., 24, (1994) 197-209.

J. Jachymski, On probabilistic $varphi$-contractions on Menger spaces, Nonlinear Anal., 73, (2010) 2199-2203.

P.K. Jhade and A.S. Saluja, Common fixed points theorem for nonexpansive type single valued mappings, Int. J. Nonlinear Anal. Appl., 7 (2016) No.1, 45-51.

P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of nonexpansive type multivalued and single valued maps, European J. Pure Appl. Math., 4 (2011) $330-339$.

Jun Wu, Some fixed-point theorems for mixed monotone operators in partially ordered probabilistic metric spaces, Fixed Point Theory Appl., 49 (2011).

G. Jungck, Compatible mappings and common fixed point, Intern. J. Math. Math. Sci., 9 (1986) 771-779.

R.P. Pant, Common fixed points of non-commuting mappings, J. Math. Anal. Appl., 188 (1994) 436-440.

R.P. Pant, Common fixed points for contractive maps, $J$. Math. Anal. Appl., 1226 (1998) 251-258.

R.P. Pant, R.K. Bisht and D. Arora, Weak reciprocal continuity and fixed point theorems, Ann. Univ. Ferrara, 57 (2011) $181-190$.

H.K. Pathak, Y.J. Cho and S.M. Kang, Remark on R-weak commuting mappings and common fixed point theorems, Bull. Korean Math. Soc., 34 (1997) 247-257.

B. Samet, M. Rajovic, et al., Common fixed-point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl., 71 (2011).

B. Schweizer, A. Sklar, Probabilistic Metric Spaces, North-Holland, New York (1983).

VM. Sehgal, AT. Bharucha-Reid, Fixed points of contraction mappings on PM-spaces, Math. Syst. Theory, 6, (1972) 97-102.

S. Sessa, On a weak commutativity condition of mappings in fixed point consideration, Publ. Inst. Math., $32(1982) 129-153$.

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Published

01-07-2018

How to Cite

Razieh Farokhzad Rostami. “Coincidence Fixed Point Theorem in a Menger Probabilistic Metric Spaces”. Malaya Journal of Matematik, vol. 6, no. 03, July 2018, pp. 499-05, doi:10.26637/MJM0603/0007.