FIXED POINT

× 0, ∞ satisfying thefollowing conditions, for each x, y, z ∈ X and t, s > 0:FM-1 Mx, y, t > 0;FM-2 Mx, y, t1 if and only if x  y;FM-3 Mx, y, tMy, x, t;FM-4 Mx, y, t ∗ My, z, s ≤ Mx, z, t  s;FM-5 Mx, y, · : 0, ∞ → 0, 1 is continuous.Let X, M, ∗ be[r]

Let A : C → H be a mapping. The classical variational inequality, denoted byVIA, C,istofindx∗∈ C such thatAx∗,v− x∗≥ 0, ∀v ∈ C. 1.22 Fixed Point Theory and ApplicationsThe variational inequality has been extensively studied in the literature see, e.g., 1–3.Themapping A is call[r]

[16] H. K. Xu and T. H. Kim, “Convergence of hybrid steepest-descent methods for variational in-equalities,” Journal of Optimization Theory and Applications, vol. 119, no. 1, pp. 185–201, 2003.10 Fixed Point Theory and Applications[17] T. Suzuki, “Strong convergence of Krasnoselskii an[r]

This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon.Fixed point theorems for mappings with condition (B)Fixed Point Theory and Applications 2011, 2011:92 doi:10.1186/1[r]

Fixed Point Theory and Applications for giving us the opportunity to edit this special issue.Anthony To-Ming LauTomonari Suzuki

 y,sof and T satisfy the hypothesesof all theorems and corollaries in 1,butf and T have no common fixed point.Thus, it is not surprising that there are a number of papers involving hybrid pairs inwhich the conclusion of the theorems is not a common fixed point, but a common coincidenc[r]

This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon.On generalized weakly directional contractions and approximate fixed pointproperty with applicationsFixed Point Theory and Applic[r]

[4] Y C. Lin, “Three-step iterative convergence theorems with er rors in Banach spaces,” Ta iwa ne seJournal of Mathematics, vol. 10, no. 1, pp. 75–86, 2006.[5] L C. Zeng, G. M. Lee, and N C. Wong, “Ishikawa iteration with errors for approximating fixedpoints of strictly pseudocontractive mappings of[r]

This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon.On generalized weakly directional contractions and approximate fixed pointproperty with applicationsFixed Point Theory and Applic[r]

1(x, y,z), for all x, y, z Î X, S, T : X × X ® X, and f : X ® X be mappings satisfyingG1S(x, y), T(u, v), T(s, t) ≤ hG2(fx, fu, fs)(2:21)for all x, y, u, v, s, t Î X, where 0 ≤ h <1.IfS(X × X) ⊆ f(X), T(X × X) ⊆ f(X), f(X)isG1-complete subset of X,thenS, T,andf have a unique common coupled[r]

Appl. 60, 2508–2515 (2010)25. Mustafa, Z, Sims, B: A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 7, 289–297(2006)26. Abbas, M, Rhoades, BE: Common fixed point results for non-commuting mappings without continuityin generalized metric spaces. Appl. Math. Comput. 215, 26[r]

This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon.Nonlinear coupled fixed point theorems in ordered generalized metric spaceswith integral typeFixed Point Theory and Applic[r]

The authors declare that they have no competing interests.Authors’ contributionsZL carried out the main part of this article. All authors read and ap-proved the final manuscript.AcknowledgmentsThis study was supported by the National Natural Science Foundation ofChina (10701040,11161022,60964005), th[r]

2000 MSC: 54H25; 47H10; 54E50.Keywords: ordered set; coupled coincidence point; coupled common fixed point; generalized metric space;altering distance function; weakly contractive condition; contraction of integral type.11 IntroductionFixed points of mappings in ordered metric space are[r]

The authors declare that they have no competing interests.Authors’ contributionsZL carried out the main part of this article. All authors read and ap-proved the final manuscript.AcknowledgmentsThis study was supported by the National Natural Science Foundation ofChina (10701040,11161022,60964005), th[r]

[21] Abbas, M, Nazir, T, Radenovi´c, S: Common fixed points of four maps inpartially ordered metric spaces. Appl. Math. Lett. 24, 1520–1526 (2011)[22] Altun, I, Simsek, H: Some fixed point theorems on ordered metric spacesand application. Fixed Point Theory Appl. 2010 Article ID 6[r]

Proposition (40): A set E ⊆ V , with V a normed space, is compact if and only if E is closedand relatively compact.Proposition (41): Relatively compact sets are bounded in normed spaces.Proposition (42): In finite dimensions:• closed and bounded sets are compact.• bounded sets are relatively compact.[r]

precompact-inducing subadmissible subset of X.Applying Proposition 1.3, 1.4,andRemark 1.5, we are easy to conclude the followingcorollary.Corollary 2.3. Let X be a nonempty bounded subadmissible subset of a metric space M, d.IfT : X → 2Xis a generalized comparison (comparison) type ψ-set contracti[r]

AcknowledgementsThe first author was supported by the Natural Science Foundation of Yunnan Province (2010ZC152) and the ScientificResearch Foundation from Yunnan Province Education Committee (08Y0338); the second author was supportedpartially by grant no. NSC 100-2115-M-017-001 of the National Scien[r]

[4] Razani, A, Nabizadeh, E, Beyg Mohamadi, M, Homaeipour, S: Fixed pointof nonlinear and asymptotic contractions in the modular space. Abstr. Appl.Anal. 2007, Article ID 40575, 10 (2007)[5] Rhoades, BE: Some theorems on weakly contractive maps. Nonlinear Anal.47, 2683–2693 (2001)[6] Sintunav[r]