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Turkish Journal of Analysis and Number Theory

**ISSN (Print):**
2333-1100

**ISSN (Online):**
2333-1232

**Frequency:**
bimonthly

**Editor-in-Chief:**
Mehmet Acikgoz, Feng Qi, Cenap ozel

**Website:**
http://www.sciepub.com/journal/TJANT

### Article

**Some Fixed Point Results on Multiplicative (b)-metric-like Spaces**

^{1}Department of Mathematics, University of Peshawar, Peshawar, Pakistan

*Turkish Journal of Analysis and Number Theory*. 2016, 4(5), 118-131

doi: 10.12691/tjant-4-5-1

Copyright © 2016 Science and Education Publishing

**Cite this paper:**

Bakht Zada, Usman Riaz. Some Fixed Point Results on Multiplicative (b)-metric-like Spaces.

*Turkish Journal of Analysis and Number Theory*. 2016; 4(5):118-131. doi: 10.12691/tjant-4-5-1.

Correspondence to: Bakht Zada, Department of Mathematics, University of Peshawar, Peshawar, Pakistan. Email: bakhtzada56@gmail.com, bakhtzada56@yahoo.com

### Abstract

### Keywords

**Partial metric space, metric-like space, b-metric space, b-metric-like space, fixed point, integral equation**

### References

[1] | M. A. Alghamdi, N. Hussain, and P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces. Journal of Inequalities and Applications, article 402, (2013). | ||

[2] | Agarwal, El-Gebeily, ORegan, Generalized contractions in partially ordered metric spaces. Appl. Anal., (2008). | ||

[3] | A. E. Bashirov, E. M. Kurpinar, A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36-48. | ||

[4] | S. Czerwik, Contraction mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 1, (1993). | ||

[5] | Daffer, Kaneko, On expansive mappings. Math. Jpn. (1992). | ||

[6] | Ozavsar, Cevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces. arXiv:1205.5131v1 [math.GM] (2012). | ||

[7] | Edelstein, On fixed and periodic points under contractive mappings. J. Lond. Math. Soc. 37, (1962). | ||

[8] | S. Gaulyaz, E. Karapinar and V. Rakocevic and P. Salimi, Existence of a solution of integral equations via fixed point theorem. Journal of Inequalities and Appl, (2013). | ||

[9] | Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points. Fixed Point Theory and Applications, (2012). | ||

[10] | Kirk,WA, Srinavasan, PS, Veeramani, Fixed points for mapping satisfying cyclical contractive conditions. Fixed Point Theory 4, (2003). | ||

[11] | Kumar, Garg, Expansion mapping theorems in metric spaces. Int. J. Contemp. Math. Sci. (2009). | ||

[12] | S. G. Matthews, Partial metric topology. Annals of the New York Academy of Sciences. General Topology and Applications, vol. 728, (1994). | ||

[13] | H. K. Pathak, M. S. Khan and R. Tiwari, A common fixed point theorem and its application to nonlinear integral equations. Computers and Mathematics with Applications, (2007). | ||

[14] | H. K. Pathak, S. N. Mishra and A. K. Kalinde, Common xed point theorems with applications to nonlinear integral equations. Demonstratio Math., XXXII (1999). | ||

[15] | S. Shukla, Partial b-metric spaces and fixed point theorems. Mediterranean Journal of Mathematics, (2013). | ||

[16] | Suzuki, A new type of fixed point theorem in metric spaces. Nonlinear Anal. 71(11), (2009). | ||

### Article

**Some Integral Inequalities of the Hermite-Hadamard Type for Strongly Quasi-convex Functions**

^{1}College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia Autonomous Region, China

^{2}School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, China

*Turkish Journal of Analysis and Number Theory*. 2016, 4(5), 132-134

doi: 10.12691/tjant-4-5-2

Copyright © 2016 Science and Education Publishing

**Cite this paper:**

Yi-Xuan Sun, Jing-Yu Wang, Bai-Ni Guo. Some Integral Inequalities of the Hermite-Hadamard Type for Strongly Quasi-convex Functions.

*Turkish Journal of Analysis and Number Theory*. 2016; 4(5):132-134. doi: 10.12691/tjant-4-5-2.

Correspondence to: Bai-Ni Guo, School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, China. Email: bai.ni.guo@gmail.com, bai.ni.guo@hotmail.com

### Abstract

### Keywords

### References

[1] | Dragomir, S. S., Pečarić, J., and Persson, L. E., Some inequalities of Hadamard type, Soochow J. Math., 21 (3) (1995), 335-341. | ||

[2] | Polyak, B. T., Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl., 7 (1966), 72-75. | ||

[3] | Dragomir, S. S. and Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95. | ||

[4] | Ion, D. A., Some estimates on the Hermite--Hadamard inequality through quasi-convex functions, Ann. Univ. Craiova Math. Comp. Sci. Ser., 34 (2007), 82-87. | ||

[5] | Alomari, M., Darus, M., and Kirmaci, U. S., Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and special means, Comput. Math. Appl., 59 (2010), 225-232. | ||

### Article

**Inequalities of Type Hermite-Hadamard for Fractional Integrals via Differentiable Convex Functions**

^{1}Department of Mathematics, College of Education, Sulaimani University, Sulaimani, Kurdistan Region, Iraq

*Turkish Journal of Analysis and Number Theory*. 2016, 4(5), 135-139

doi: 10.12691/tjant-4-5-3

Copyright © 2016 Science and Education Publishing

**Cite this paper:**

P. O. Mohammed. Inequalities of Type Hermite-Hadamard for Fractional Integrals via Differentiable Convex Functions.

*Turkish Journal of Analysis and Number Theory*. 2016; 4(5):135-139. doi: 10.12691/tjant-4-5-3.

Correspondence to: P. O. Mohammed, Department of Mathematics, College of Education, Sulaimani University, Sulaimani, Kurdistan Region, Iraq. Email: pshtiwansangawi@gmail.com

### Abstract

### Keywords

### References

[1] | J. Hadamard, Étude sur les propriétés des fonctions entières en particulier d'une function considérée par Riemann, J Math Pures Appl, 58 (1893), 171-215. | ||

[2] | M. Tomar, E. Set and M. Z. Sarıkaya, Hermite-Hadamard type Riemann-Liouville fractional integral inequalities for convex functions, AIP Conference Proceedings 1726, 020035 (2016). | ||

[3] | Z. Dahmani, On Minkowski and Hermite-Hadamad integral inequalities via fractional integration, Annals of Functional Analysis, 1(1) (2010), 51-58. | ||

[4] | M. Tunç, Y. Subas and I. Karabayir, On some Hadamard type inequalities for MTconvex functions, Int. J. Open Probl. Comput. Sci. Math., 6 (2013), 102-113. | ||

[5] | S. Qaisar and S. Hussain, Generalization of integral inequalities of the type of Hermite-Hadamard through invexity, Malaya J. Mat., 3(1) (2015), 99-109. | ||

[6] | J. Park, Fractional Hermite-Hadamard-like Type Inequalities for Convex Functions, International Journal of Mathematical Analysis, 9(29) (2015), 1415-1429. | ||

[7] | Z. Lin, J. Wang and W. Wei, Fractional Hermite-Hadamard inequalities through r-convex functions via power means, Ser. Math. Inform., 30(2) (2015), 129-145. | ||

[8] | M. Z. Sarikaya, H. Yaldiz and H. Budak, Some integral inequalities for convex stochastic processes, Acta Math. Univ. Comenianae, LXXXV(1) (2016), 155-164. | ||

[9] | I. Podlubni, Fractional Differential Equations, Academic Press, San Diego, 1999. | ||