Some common fixed point theorems in partially ordered P-metric spaces

Subject Areas : Statistics

H.  Hosseinzadeh ¹ (Department of Mathematics, Ardebil Branch, Islamic Azad University, Ardebil, Iran)
V.  Parvaneh ² (Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-EGharb, Iran)

Received: 2019-01-02 Accepted : 2019-07-06 Published : 2020-08-22

Keywords: فضای متری تعمیم یافته, فضای مرتب جزیی, P-متری, نقطه ثابت,

Abstract :

A new and attractive metric space is a P-metric space which is a generalization of the concept of b-metric spaces. The generalization of the principle of Banach contraction has been carried out by many authors. Generalizations focus on the extension of metric spaces and the extension of contraction conditions. A few metrics, such as partial metrics, G-metrics, 2-metrics and Branciari metrics are some examples of metrics provided in this field. The aim of this paper is to present some common fixed point results for two mappings (one of them is weakly isotone increasing with respect to another) in the framework of ordered $p$-metric spaces. Our results are generalizations of the presented results in [H. K. Nashine, B. Samet and C. Vetro, Math. Comput. Modelling, 54 (2011) 712–720] and [ J.R. Roshana, V. Parvaneh and Z. Kadelburg, J.Nonlinear Sci. Appl., 7 (2014), 229--245]. An example is also provided to support our results.

References:

 

[1]. H. K. Nashine, B. Samet and C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Modelling, 54 (2011), 712-720

 

[2]. J.R. Roshana, V. Parvaneh and Z. Kadelburg, Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 229--245.

 

[3]. V. Parvaneh, Fixed points of -contractive mappings in ordered -metric spaces, submitted.

 

[4]. M. Abbas, T. Nazir and S. Radenovic, Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Letter. 24 (2011), 1520-1526.

 

[5]. M. Abbas, V. Parvaneh and A. Razani, Periodic point of T-Ciric generalized contraction mappings in ordered metric spaces. Georgian Math. J. 19 (2012, No.4, 597-610.

 

[6]. R. P. Agarwal, M. A. El-Gebeily and D. O'Regan, generalized contractions in partially ordered metric spaces, Applicable Analysis, 87 (1) (2008), 109-116.

 

[7]. A. Aghajani, M. Abbas and J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered -metric spaces, Mathematica Slovaca, Accepted.

 

[8]. A. Aghajani, S. Radenovic, J.R. Roshan, Common fixed point results for four mappings satisfying almost generalized -contractive condition in partially ordered metric spaces, Appl. Math. Comput, 218 (2012), 5665--5670.

 

[9]. M. Akkouchi, Common fixed point theorems for two selfmappings of a -metric space under an implicit relation, Hacettepe journalof Mathematics Stat, 40 (6) (2011), 805-810.

 

[10]. H. Aydi, M. Bota, E. Karapinar and S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in -metric spaces, Fixed Point Theory and Applications, 2012: 88. 2012.

 

[11]. M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two -metrics, Studia Univ., Babes-Bolyai, Mathematica, Volume LIV, Number 3, (2009).

 

[12]. M. Boriceanu, Strict fixed point theorems for multivalued operators in -metric spaces, Int. J. Modern Math., 4 (3) (2009), 285-301.

 

[13]. M. Boriceanu, M. Bota and A. Petrusel, Multivalued fractals in -metric spaces, Cent. Eur. J. Math., 8 (2) (2010), 367-377.

 

[14]. M. Bota, A. Molnar and C. Varga, On Ekeland's variational principle in -metric spaces, Fixed Point Theory, 12 (2) (2011), 21--28.

 

[15]. S. Czerwik, Nonlinear set-valued contraction mappings in -metric spaces, Atti Sem. Mat. Fis. Univ. Modena. 46 (2) [1]. (1998), 263-276.

 

[16]. J. Esmaily, S. M. Vaezpour and B.E.. Rhoades, Coincidence point theorem for generalized weakly contractions in ordered metric spaces, Appl. Math. Comput., 219 (2012), 1536-1548.

[17]. J. Harjani and K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (3-4) (2010), 1188-1197.

 

[18]. H. Hosseinzadeh, Fixed point theorems on soft metric spaces, Journal of Fixed Point Theory and Applications, 19(2)(2017),1625-647.

 

[19]. H Hosseinzadeh, A Jabbari, A Razani,  Fixed-Point Theorems and Common Fixed-Point Theorems on Spaces Equipped With Vector-Valued Metrics, Ukrains’ kyi Matematychnyi Zhurnal, 65(5)(2013), 734-740

 

[20]. Hussain and M. H. Shah, KKM mappings in cone -metric spaces, Comput. Math. Appl, 62 (2011), 1677-1684.

 

[21]. M. A. Khamsi and N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (9) (2010), 3123-3129.

 

[22]. H. K. Nashine and B. Samet, Fixed point results for mappings satisfying -weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 2201-2209.

 

[23]. J. J. Nieto and R. R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), 223-239.

 

[24]. J. J. Nieto, R. L. Pouso and R. Rodriguez-Lopez, Fixed point theorems in ordered abstract sets, Proc. Amer. Math. Soc., 135 (2007), 2505-2517.

 

[25]. J. J. Nieto and R. Rodriguez-Lopez, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 2205-2212.

 

[26]. M. O. Olatinwo, Some results on multi-valued weakly jungck mappings in -metric space, Cent. Eur. J. Math, 6 (4) (2008), 610-621.

 

[27]. M. Pacurar, Sequences of almost contractions and fixed points in -metric spaces, Analele Universitatii de Vest, Timisoara Seria Matematica Informatica XLVIII, 3 (2010), 125-137.

 

[28]. S. Radenovic and Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Compu. Math. Appl, 60 (2010), 1776-1783.

 

[29]. A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.

 

 

[30]. A Razani, H Hosseinzadeh, Triple fixed point theorems on FLM algebras, Fixed Point Theory and Applications, 1(2013),16.

 

[31]. A.Razani. Results in Fixed Point Theory, Andisheh Zarin publisher, Qazvin, August 2010.

 

[32]. A. Razani, R. Moradi. Fixed point theory in modular space, Saieh Ghostar Publisher, Qazvin, April 2006.