FIXED POINT AND COMMON FIXED POINT RESULTS FOR EXPANSIVE MAPPINGS IN Gb- CONE METRIC SPACES

Article Sidebar

PDF
Published: Nov 3, 2015

Main Article Content

Manoj Ughade
Sarvepalli Radhakrishnan University
Rashmi Jain
J.h.college betul
R D Daheriya
J.h.college betul

Abstract

Very recently, Manoj Ughade and R D Daheriya [18] introduced the concept of -cone metric and some established some fixed point and common fixed point theorems for self-mappings satisfying various contractive conditions in -cone metric spaces without the assumption of normality. In this paper, we present a fixed point theorem for self-mappings satisfying expansive type condition -cone metric spaces without the assumption of normality. Moreover, some examples are provided to illustrate the usability of the obtained results.

Downloads

Download data is not yet available.

Article Details

How to Cite
Ughade, M., Jain, R., & Daheriya, R. D. (2015). FIXED POINT AND COMMON FIXED POINT RESULTS FOR EXPANSIVE MAPPINGS IN Gb- CONE METRIC SPACES. Journal of Global Research in Mathematical Archives(JGRMA), 2(11), 01–11. Retrieved from https://jgrma.com/index.php/jgrma/article/view/261
Issue
Vol. 2 No. 11 (2014): November-2014
Section
Research Paper
Download Copyright
Author Biographies

Manoj Ughade, Sarvepalli Radhakrishnan University

Department of Mathematics, Asst. Prof.,

Rashmi Jain, J.h.college betul

Department of mathematics

R D Daheriya, J.h.college betul

Prof,  Department of mathematics

References

B. C. Dhage, “Generalized metric space and mapping with fixed point,†Bulletin of Calcutta Mathematical Society, vol. 84, pp. 329–336, 1992.

B. C. Dhage, “On generalized metric spaces and topological structure. II,†Pure and Applied Mathematika Sciences, vol. 40, no. 1-2, pp. 37–41, 1994.

B. C. Dhage, “A common fixed point principle in D-metric spaces,†Bulletin of the Calcutta Mathematical Society, vol. 91, no. 6, pp. 475–480, 1999.

B. C. Dhage “Generalized metric spaces and topological structure. I,†Annalele Stintificeale Universitatii Al.I. Cuza, vol. 46, no. 1, pp. 3–24, 2000.

Z. Mustafa and B. Sims, “Some remarks concerning D-metric spaces,†in Proceedings of the International Conference on Fixed Point Theory and Applications, Yokohama, Japan, pp. 189–198, 2004.

Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,†Journal of Non- linear and Convex Analysis, vol. 7, no. 2, pp. 289–297, 2006.

M. Abbas and B. E. Rhoades, “Common fixed point results for non commuting mappings without continuity in generalized metric spaces,†Appl. Math. and Comp., vol. 215, no. 1, pp. 262–269, 2009.

H. Aydi, W. Shatanawi, and C. Vetro, “On generalized weakly G-contraction mapping in G-metric spaces,†Computers & Mathematics with Applications, vol. 62, pp. 4222–4229, 2011.8

H. Aydi, “A fixed point result involving a generalized weakly contractive condition in G-metric spaces,†Bulletin of Mathematical Analysis and Applications, vol. 3, no. 4, pp. 180–188, 2011.

H. Aydi, “A common fixed point of integral type contraction in generalized metric spaces,†Journal of Advanced Mathematical Studies, vol. 5, no. 1, pp. 111–117, 2012.

Duran Turkoglu and Nurcan Bilgili, Some fixed point theorem for mapping on complete G-cone metric spaces, Journal of Applied Functional Analysis, Vol.7, No’s 1-2,118-137.

Asadollah Aghajani, Mujahid Abbas, Jamal Rezaei Roshan, Common Fixed Point of Generalized Weak Contractive Mappings in Partially Ordered -metric Spaces, Filomat 28:6 (2014), 1087–1101 DOI 10.2298/FIL140 6087A.

Beg, I, Abbas, M, Nazir, T: Generalized cone metric spaces. J. Nonlinear Sci. Appl. 3(1), 21-31, 2010.

Azam, A, Arshad, M, Beg, I: Existence of fixed points in complete cone metric spaces. Int. J. Mod. Math. 5(1), 91-99, 2010.

Daheriya, R.D., Jain, R., Ughade, M., “Some Fixed Point Theorem for Expansive Type Mapping in Dislocated Metric Spaceâ€, ISRN Mathematical Analysis, Volume 2012, Article ID 376832, 5 pages, doi:10.5402/2012/376832.

Ughade, M. and Daheriya, R. D.,“Tripled fixed point results in generalized metric spaces under nonlinear type contractions depended on another function†Gazi University Journal of Science, 28(1):75-86, 2015.

Song, G-X, Sun, X-Y, Zhao, Y, Wang, G-T, “New common fixed point theorems for maps on cone metric spacesâ€. Appl. Math. Lett. 32, 1033-1037, 2010.

Manoj Ughade and R. D. Daheriya, Fixed point and common fixed point results for contraction mappings in - cone metric spaces, Gazi University Journal of Science, Accepted 2015.

A. S. Saluja, A. K. Dhakda and D. Magarde, Some fixed point theorems for expansive type mapping in dislocated metric space, Mathematical Theorey and Modeling, 3(2013).

R. D. Daheriya, Rashmi Jain, and Manoj Ughade “Some Fixed Point Theorem for Expansive Type Mapping in Dislocated Metric Spaceâ€, ISRN Mathematical Analysis, Volume 2012, Article ID 376832, 5 pages, doi:10.5402/2012/376832.

Yan Han and Shaoyuan Xu, Some new theorems of expanding mappings without continuity in cone metric spaces, Fixed Point Theory and Applications, 2013, 2013:3.

Wasfi Shatanawi and Fadi Awawdeh, Some fixed and coincidence point theorems for expansive maps in cone metric spaces, Fixed Point Theory and Applications 2012, 2012:19.

Xianjiu Huang, Chuanxi Zhu, Xi Wen, Fixed point theorems for expanding mappings in partial metric spaces, An. St. Univ. Ovidius Constant_a Vol. 20(1), 2012, 213-224.

Z. Mustafa, F. Awawdeh and W. Shatanawi, Fixed Point Theorem for Expansive Mappings in G-Metric Spaces, Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 50, 2463-2472.

A. Muraliraj and R. Jahir Hussain, Coincidence and Fixed Point Theorems for Expansive Maps in d−Metric Spaces, Int. Journal of Math. Analysis, Vol. 7, 2013, no. 44, 2171 – 2179.

P. Z. Daffer, H. Kaneko, On expansive mappings, Math. Japonica. 37 (1992), 733-735.

S. Z. Wang, B. Y. Li, Z. M. Gao, K. Iseki, Some fixed point theorems for expansion mappings, Math. Japonica. 29 (1984), 631-636.

Aage, CT, Salunke, JN: Some fixed point theorems for expansion onto mappings on cone metric spaces. Acta Math. Sin. Engl. Ser. 27(6), 1101-1106 (2011).

R. D. Daheriya, Rashmi Jain, and Manoj Ughade, Unified fixed point theorems for non-surjective expansion mappings by using class on 2- metric spaces, Bessel J. Math., 3(3), (2013), 271-291.

G. Jungck, “Commuting mappings and fixed points,†The American Mathematical Monthly, vol. 83, no.4, pp. 261-263, 1976.

G. Jungck, “Compatible mappings and common fixed points,†International Journal of Mathematics and Mathematical Sciences, vol. 9, no.4, pp. 771-779, 1986.

G. Jungck, “Fixed points for non-continuous non-self mappings on non-metric space,†Far East Journal of Mathematical Sciences, vol. 4, pp. 199-212, 1996.