Purpose This paper aims to empirically assess the contribution of Islamic banks toward the financial stability of Pakistan. For this, the authors investigate the relative financial strength of Islamic banks and their contribution toward the financial stability. They also examine the relationship between the competitive conduct of banks and banking system stability. Design/methodology/approach The authors use quarterly data of ten conventional banks, four full-fledged Islamic banks and six standalone Islamic branches of conventional banks of Pakistan for the period 2006-2012. The z-score has been computed and used as the measure of stability of banks and the random effects estimator applied to quantify the impact of bank-specific variables and macroeconomic indicators on the financial stability. The empirical framework used in the paper enables the authors us to examine the differential effect of each underlying variable on the financial stability across Islamic and conventional banks. To check the robustness of the results, the authors have estimated several models with different specifications. Findings The regression results indicate that income diversity, profitability ratio, loan to asset ratio, asset size and the market concentration ratio of banks have significant effects on the stability of banks. Comparing Islamic and conventional banks, notable differential effects of the empirical determinants of financial stability for Islamic and conventional banks have been observed. The results suggest that Islamic banks have performed better as compared to conventional banks and contributed more effectively in the stability of financial sector. Overall, the results depict that the contribution of Islamic banks toward the financial stability has been reasonable and prospective. Practical implications The empirical results of the paper are very useful not only for banks’ managements but also for the investors, bank customers and policymakers. Specifically, the findings help in enhancing our understanding as to how the bank-specific variables and macroeconomic indicators are related to the financial stability of the banking system. The results also help understand the role of both Islamic and conventional banks in the financial stability. Further, the results suggest that the financial soundness can be enhanced by creating healthy competition in the banking industry. The results about macroeconomic indicators imply that protective measures are required to intensify (mitigate) the positive (negative) effect of gross domestic product (inflation) on banks’ financial stability. Originality/value This paper provides an overall comparative analysis of financial stability of both Islamic and conventional banks of Pakistan. First, the paper computes the z-score for each bank included in the sample, and then, it performs the regression analysis to study how bank-specific variables and macroeconomic factors are related to the financial stability of banks. Unlike the previous studies, our empirical framework enables the authors to examine the differential effect of each underlying variable on the financial stability across Islamic and conventional banks.

In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.

In the present study, fractional variants of Hermite–Hadamard, Hermite–Hadamard–Fejér, and Pachpatte inequalities are studied by employing Mercer concept. Firstly, new Hermite–Hadamard–Mercer-type inequalities are presented for harmonically convex functions involving fractional integral operators with exponential kernel. Then, weighted Hadamard–Fejér–Mercer-type inequalities involving exponential function as kernel are proved. Finally, Pachpatte–Mercer-type inequalities for products of harmonically convex functions via fractional integral operators with exponential kernel are constructed.

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In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional integrals. As a result, we introduce several related fractional inequalities connected with the right and left differences of obtained new inequalities for differentiable harmonically convex mappings. As an application viewpoint, new estimates regarding hypergeometric functions and special means of real numbers are exemplified to determine the pertinence and validity of the suggested scheme. Our results presented here provide extensions of others given in the literature. The results proved in this paper may stimulate further research in this fascinating area.